What is the reason AMD Radeon is not widely used for machine learning and deep learning?
The main reason that AMD Radeon graphics card is not used for deep learning is not the hardware and raw speed. Instead it is because the software and drivers for deep learning on Radeon GPU is not actively developed. NVIDIA have good drivers and software stack for deep learning such as CUDA, CUDNN and more. Many deep learning library also have CUDA support. However for AMD there is little support on software of GPU. There is ROCM but it is not well optimized and also a lot of deep learning libraries don't have ROCM support.

Also on the hardware side, AMD lacks deep learning specific features like tensor cores. AMD also don't have data centre specific cards like the Tesla lineup. The performing of AMD cards also is not very good until recently with the RDNA architecture.

Lastly, data centres don't change hardware very often. NVIDIA flourished in the deep learning field very early on so many companies bought a lot of Tesla GPU. Even if AMD caught up in the deep learning field it is very hard as many companies have used NVIDIA from a long time ago, and switching to a very different architecture of GPU is troublesome, especially for a data centre with couple hundred or more servers. 

AMD has also "given up" on deep learning market. They don't actively tries to make effort in deep learning data centres using AMD hardware. Many data centre also use very old Tesla hardwares like Tesla K80 of M series. 

Hope this can help you.